This invention relates generally to thermoelectric heating and cooling and more particularly to an improved method of designing thermoelectric device so that it exhibits the best possible performance characteristics.
Thermoelectric heating and cooling devices operate on the basis of a thermodynamic principle known as the Peltier effect. This phenomenon results in the generation of a temperature difference between junctions of two dissimilar materials when a direct current is passed through the materials. One junction is increased in temperature and can transfer heat to a fluid passed in thermal contact with it. The other junction is cooled and can absorb heat from a fluid. Thus, a thermoelectric device can be operated as a heat pump and has the advantage of solid state components because of the absence of moving parts.
The heat pumping capacity of two dissimilar thermoelectric materials, referred to as a couple, is usually very small so that it is necessary in actual practice to combine a number of couples to form a component known as a thermoelectric module. The number of couples in a module can vary widely and is typically between 3 and 127. A practical thermoelectric device normally requires between 10 and 100 modules in order to meet the heat pumping requirements. The heat which is delivered to the hot faces of the thermoelectric modules is transferred to a fluid passed through a hot side heat exchanger, while another fluid is passed through a cold side heat exchanger to transfer heat from the fluid to the cold faces of the modules.
Different thermoelectric devices may vary widely in configuration, depending upon numerous factors such as the types of fluids used (gas and liquid, gas and gas, or liquid and liquid) and the main purpose of the device (heating only, cooling only, or both heating and cooling). However, in essence, all thermoelectric devices include a closed channel for the process fluid and a number of thermoelectric modules each having one face (hot or cold) in thermal contact with the channel. The other face of each module is in thermal contact with the surfaces of a heat exchanger which receives a second fluid and which normally has fins or other elements that promote heat transfer. The heat exchanger is usually an open flow unit.
In the past, the design of thermoelectric heating/cooling devices for a particular application has been based merely on the characteristics of the thermoelectric properties of the modules. To my knowledge, attempts have not been made to interface or interrelate the thermoelectric characteristics with the heat transfer processes which occur on the hot and cold sides of the modules. Thus, the fact that the process fluid and the other fluid both undergo temperature changes as they flow through the process channel and heat exchanger, respectively, is not taken into account, and significant errors can result.
In accordance with conventional practice, single stage thermoelectric devices are designed by making certain assumptions. The thermoelectric property values, such as the Seebeck coefficient (.alpha.), the electrical resistivity (.rho.) and the thermal conductivity (k) of the materials, are assumed to be constant and are taken at the mean of the hot junction temperature and cold junction temperature.
The conventional method used to design the components of thermoelectric devices involves two phases, the first of which entails three steps having the purpose of determining the optimum values of the major thermoelectric design factors herein represented by the symbols H and .mu.. The factor H is given by the equation EQU H=I/.upsilon. (1)
where I is the current flow through a couple and .upsilon. is the ratio of the cross-sectional area of a thermoelectric element to its height. The second factor .mu. is defined by the equation EQU .mu.=n.upsilon. (2)
where n is the total number of thermoelectric couples required in the device to satisfy the design requirements for heating and/or cooling. It is highly important that the factors H and .mu. be optimally designed, because even small errors or allowances in either factor can significantly affect the performance of the thermoelectric device.
The first step in the conventional design process is to estimate the average temperature of the hot junction (T.sub.h) and the average temperature of the cold junction (T.sub.c) of the thermoelectric modules. There is no accepted method for determining these values, and various approximations are made based on factors such as the inlet temperatures of the process fluid and the second fluid, the heat transfer rate of the process fluid channel, and the heat transfer rate of the heat exchanger. Because of the lack of any established procedure for arriving at an accurate estimation of the values for T.sub.h and T.sub.c, the values that are used for these temperatures are often considerably different from the temperatures that are experienced in the actual device. Consequently, this step in the conventional design procedure often leads to significant errors.
The second step involves calculating the optimum values of H depending upon whether the system is designed to deliver the highest possible coefficient of performance (COP) or the highest possible heating/cooling capacity. To obtain maximum COP, the optimum value of H can be calculated by solving the equation: EQU H=.alpha.(T.sub.h -T.sub.c)/[.rho.(w-1)], (3)
where w=[1+.alpha..sup.2 (T.sub.h +T.sub.c)/2.rho.k].sup.1/2.
To obtain maximum cooling capacity, the optimum value of H is given by: EQU H=.alpha.T.sub.c /.rho. (4)
The final step in the first phase of the conventional design procedure is to calculate the values for .mu., the total power required (P) and the COP by the following equations: EQU .mu.=Q.sub.c /[.alpha.T.sub.c H-1/2H.sup.2 .rho.-k(T.sub.h -T.sub.c)](5) EQU P=.mu.[.alpha.(T.sub.h -T.sub.c)H+H.sup.2 .rho.] (6) EQU COP=Q.sub.c /P (7)
where Q.sub.c is the desired cooling capacity.
The second phase of the conventional procedure involves calculating the number of couples (n) required in the device. This calculation is made in the same manner as in the procedure of the present invention, which will subsequently be described.
The primary conceptual problem with the conventional procedure is its failure to account for the changes in temperature that occur in the process fluid and the second fluid as they travel through the process stream channel and the heat exchanger, respectively. For example, if the process fluid is cooled, its temperature decreases continuously as it passes through the process channel. Conversely, the second fluid increases continuously in temperature as it moves past the fins of the heat exchanger. Because of this spatial variation in the temperatures of the fluid, the temperatures of the hot and cold sides of the thermoelectric modules are position-dependent. Thus, the hot junction temperature is not one single value and the cold junction temperature is likewise not a single fixed value. Because the conventional method of design involves assumptions that these temperatures are constant when in fact they are not, errors inevitably occur and the dimensions of the thermoelectric elements in the module are no optimum for the device.